Towards the start of MTTs they play fairly similar to cash games, where stacks are deep. However, the real difference comes towards the end of MTTs when players don't have many big blinds left and it turns into a push/fold game pre-flop. Obviously, this never happens in a cash game as the blinds never change, so that's the only real difference.
Also, if you are playing $1 MTTs or the 50c ones, you will notice a lot of idiots who will shove pre-flop early in the tournament with a deep stack, which they probably wouldn't do in a cash game due to it being actual money on the table. Obviously the thought of losing tournament chips isn't as frightening for them as losing $2.